A fluid solver using signed distance function (SDF) for shape representation was developed based on the immersed boundary method to simulate incompressible viscous flows. The forcing velocities near boundary are extrapolated by trilinear interpolation with taking into account a boundary condition using SDF. SMAC method is employed for solving basic equations for unsteady incompressible flows. The equations are discretized in space by 2nd-order central difference method, where the discretization near boundary is improved by SDF to satisfy a Dirichlet boundary condition for velocity. The fluid solver was verified in both steady and oscillating three-dimensional Poiseuille flows. As the grid spacing decreases, L² and L^∞ norm of the error of the axial velocity profile respectively decrease by the order of 1.96 and 1.89 for the oscillating flow. Therefore, the fluid solver enables to analyze the Poiseuille flow using Cartesian mesh by 2nd-order of accuracy in space.